Press on first-rate vessel from island (8)
I believe the answer is:
jamaican
'from island' is the definition.
(Jamaica is an island)
'press on first-rate vessel' is the wordplay.
'press' becomes 'jam' (synonyms).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'first rate' becomes 'AI' (resembles Aj, old-fashioned slang for very good).
'vessel' becomes 'can' (type of container).
'jam'+'ai'+'can'='JAMAICAN'
(Other definitions for jamaican that I've seen before include "Caribbean island resident" , "One from Kingston, say" , "Islander" , "From Kingston, perhaps" , "Eg, native of Kingston" .)